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function woocommerce_subcats_from_brand( $product_parent_cat_NAME, $title_widget ) {
  global $wpdb, $post;

  //$IDbyNAME = get_term_by('slug', $parent_cat_NAME, 'product_cat');
  //$product_cat_ID = $IDbyNAME->term_id;

  $IDproductByNAME = get_term_by('slug', $product_parent_cat_NAME, 'product_cat');
  $product_parent_cat_ID = $IDproductByNAME->term_id;

    $args = array(
       'hierarchical' => 1,
       'show_option_none' => '',
       'hide_empty' => 0,
       'parent' => '',
       'taxonomy' => 'product_brand'
    );
  $brands = get_categories($args);
 	echo '<div class="widget woocommerce widget_product_categories"><h3>'. $title_widget .'</h3>';
    echo '<ul class="product-categories parent" >';
      foreach ($brands as $brand) {
        $link = get_term_link( $brand->slug, $brand->taxonomy );
        echo '<li class="cat-item cat-parent parent"><a href="'. $link .'">'.$brand->name.'</a></li>';

        $sql = "SELECT DISTINCT wt.* FROM wp_posts p
							INNER JOIN wp_term_relationships r ON r.object_id=p.ID
							INNER JOIN wp_term_taxonomy t ON t.term_taxonomy_id = r.term_taxonomy_id
							INNER JOIN wp_terms wt on wt.term_id = t.term_id
							WHERE p.ID IN (
								SELECT post.ID FROM  `wp_posts` as post
								INNER JOIN wp_term_relationships rs ON rs.object_id = post.ID 
								WHERE  `post_type` =  'product'
								AND  `post_status` =  'publish'
								AND rs.term_taxonomy_id  = ". $brand->term_id ."
							) AND t.taxonomy='product_cat' 
							AND t.parent = " . $product_parent_cat_ID;

 		$prod_categories = $wpdb->get_results( $sql );

 		// VISUALIZZO IL SOTTO MENU DEL BRAND

 		

 		$view_brand = false;
 		if( isset($_GET['product_brand']) AND ($_GET['product_brand'] == $brand->slug) ) {
 			$view_brand = true;
 		}
 		if( is_singular('product') ) {
 			$current_brands = get_the_terms( $post->ID, 'product_brand', true);
 			foreach ($current_brands as $current_brand) {
 				if($current_brand->slug == $brand->slug) $view_brand = true;
 			}
 		}

 		if( $prod_categories AND $view_brand ) {
 		echo '<ul class="children">';
 		foreach ($prod_categories as $prod_category) {
 			echo '<li class="cat-item"><a href="'. get_site_url() .'?product_brand='. $brand->slug .'&product_cat='. $prod_category->slug .'">'. $prod_category->name .'</a></li>';
 		} 
 		echo '</ul>';
 		echo '</div>';
 		}
      }
    echo '</ul>';
}

// Add Shortcode
function lista_brands( $atts ) {

	// Attributes
	$attr = shortcode_atts(
		array(
			'parent_products' => '',
			'title_widget' => ''
		), $atts );

	// Code
	woocommerce_subcats_from_brand($atts['parent_products'], $atts['title_widget']);

}
add_shortcode( 'ipac-lista-brands', 'lista_brands' );